A Single-Phase-to-Ground Fault Detection Method Based on the Ratio Fluctuation Coefficient of the Zero-Sequence Current and Voltage Differential in a Distribution Network

Because the traditional zero-sequence overcurrent protection method is not effective in detecting single-phase-to-ground faults (SPGF) in a low-resistance grounded system (LRGS), this paper analyzes the fault characteristics of a 10-kV LRGS in detail. From the perspective of the time domain, the relationship between zero-sequence current and zero-sequence voltage is deduced, and the characteristics corresponding to faulty lines and nonfaulty lines are analyzed. The analysis reveals that the ratio fluctuation coefficients of the zero-sequence current to the differential zero-sequence voltage corresponding to faulty lines and nonfaulty lines have notably different characteristics; consequently, a high-sensitivity SPGF detection method is proposed. This method considers the existence of unbalanced loads and asymmetric parameters in the distribution network, can effectively identify high-impedance faults as high as 5000 $\Omega $ and nonlinear arc grounding faults, and can resist noise interference with a signal-to-noise ratio of 20 dB. Finally, many simulations and comparisons based on PSCAD/EMTDC verify that the proposed detection method has better applicability than the existing methods in detecting high-impedance SPGFs.


I. INTRODUCTION
As the proportion of cable lines in large and medium-sized urban distribution networks is rapidly increasing, when a single-phase-to-ground fault (SPGF) occurs in a resonant grounded system, it may form an overvoltage arc, damage the equipment insulation, and affect the power supply reliability [1], [2]. Considering these effects, the low-resistance grounded system (LRGS) is becoming increasingly popular in large and medium-sized cities in China because it can effectively reduce the overvoltage amplitude, quickly cut the fault line, and limit the fault area [3].
SPGFs are the most common faults in distribution networks [4]. In general, an SPGF in an LRGS can produce a The associate editor coordinating the review of this manuscript and approving it for publication was Barbara Guidi . high faulty current, which is easy to detect using a protection device. However, when a high-impedance SPGF occurs, the fault is difficult to detect and remove because the faulty current is low [5], [6]. In LRGS, zero-sequence current protection is usually used to accommodate SPGFs, but it cannot effectively detect high-impedance SPGFs. The detection of high-impedance SPGFs have long been a challenging issue in distribution network. However, most of the existing research aims at resonant grounded systems or neutral ungrounded systems. For LRGS, the problem of high-impedance SPGF detection has received increasing attention in recent years. However, the existing methods for resonant grounded systems are not fully applicable because LRGSs have different characteristics from resonant grounded systems.
Therefore, some studies have used voltage to investigate high-impedance SPGFs in LRGSs. A detection method that VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ computes the zero-sequence power factor of a line to discriminate the line state with the assistance of single-phase instantaneous reactive power theory and the 4th-order components of the instantaneous active power is proposed in [7], which provides a reference value. Reference [8] introduced the improved idea of using a high-precision transformer, adaptively adjusting the current setting value, and using transient information and substation area information to detect high-impedance SPGF. Reference [9] proposed SPGF protection for LRGS based on zero-sequence voltage ratio braking, which improves the sensitivity of high-resistance grounded faults. Reference [10] calculated and analyzed the fault current when an SPGF occurred at the head and end of the feeder and proposed a staged zero-sequence overcurrent protection with high sensitivity. However, these two methods cannot sufficiently withstand high faulty impedance. Reference [11] proposed a detection method of high-impedance SPGF based on the differential current of zero-sequence current projection and neutral point current in an LRGS. This method has high sensitivity and reliability but does not consider the problem that noise may affect the acquired signal. Traditional zero-sequence current protection only uses the current amplitude, but the current phase also contains effective fault information. Reference [12] proposed a comprehensive protection method that combined the amplitude comparison and phase comparison of zero-sequence current, which can be applied to both high-impedance SPGFs and bus ground faults. Reference [13] proposed a fault line selection method that used a three-phase current three-dimensional projection fusion image as the input of a deep learning algorithm, which has a high line selection accuracy. However, for highimpedance SPGFs, the fault line selection effect must be improved when the initial fault phase angle is low. Reference [14] considered the application of 5G technology to acquire the zero-sequence current phase and proposed a fault protection scheme of an LRGS based on the ratio of zerosequence current projection components, which has good prospects, but the existing communication equipment must be modified. These methods are mainly based on the power frequency characteristics. In addition, some methods use highfrequency component information to detect high-impedance SPGFs. Reference [15] proposed a new approach for HIF detection based on the energy variation of the low harmonic orders obtained by the Stockwell transform and an adaptive threshold to ensure high sensitivity and secure detection, but it has high requirements for the computing environment. The boosted decision tree, which has high reliability, has been used to detect high-impedance SPGFs caused by vegetation, but it needs a lot of real data, as shown in experiments in [16]. Reference [17] compared the performance of signal-processing algorithms such as the ones based on the Fourier transform, Wavelet transform, Stockwell transform, and mathematical morphology for high-impedance SPGF detection, but these techniques are applied under specific conditions; for non-arc faults, the high-frequency component will be small.
Compared with zero-sequence current protection, although the existing methods improve the sensitivity, most of them do not consider the high-impedance cases in conjunction with the influence of the unbalanced distribution network. Unlike the high-voltage power grid, the high degree of unbalance is one of the main characteristics of the medium-voltage distribution network [18], which mainly refers to the imbalance of the load and imbalance of the line parameters [19]. In the normal operation state, the unbalanced zero-sequence current of the feeder is generally low, but in the unbalanced state, the voltage-current relationship at each point of the network is unlike that in the balanced state [20], [21]. With increasing fault impedance, the detection algorithm based on the relationship between voltage and current may be misevaluated [7]. Therefore, it is necessary to consider the influence of system imbalance in the research of SPGF detection algorithms.
To end these issues, an SPGF detection method based on the ratio fluctuation coefficient of the line zero-sequence current and differential zero-sequence voltage is proposed for a 10-kV LRGS in this paper. This method can effectively identify high-impedance SPGFs, and it is suitable for the cases of the line parameter asymmetry and nonlinear arc fault, and has good anti-noise ability.
The remainder of the paper is organized as follows. Section II analyzes the SPGF characteristics of a 10-kV LRGS and deduces the constraint relationship between the line zero-sequence current and the zero-sequence voltage from the perspective of the time domain. Section III introduces the basic principle, detection process, and setting principles of the detection algorithm. The simulation analysis and conclusion are presented in Sections IV and V, respectively. Fig. 1 shows a schematic diagram of an SPGF in a line of a 10-kV LRGS. In Fig. 1, the neutral point is grounded with a 10-resistance through a zigzag transformer.  When an SPGF occurs in the system, the additional state network of the fault can be decomposed into the corresponding positive-sequence, negative-sequence, and zero-sequence networks using the symmetrical component method. Fig. 2 shows the SPGF zero-sequence network of the system. C 0H1 -C 0Hn , R 0H1 -R 0Hn , and L 0H1 -L 0Hn are the zero-sequence capacitances, resistances, and inductances to ground of each nonfaulty line, C 0F is the zero-sequence capacitance to ground of the faulty line,İ 0H1 -İ 0Hn are the zero-sequence current of the nonfaulty line,İ 0F is the zero-sequence current of the faulty line, L g is the zero-sequence inductance of the zigzag transformer, and R f is the fault resistance.

II. ANALYSIS OF THE SPGF CHARACTERISTICS OF A 10-kV LRGS
According to the zero-sequence network, the equivalent zero-sequence impedance of the system can be defined as: In (2), R g is the grounded resistance of the neutral point, ω is the angular frequency of the fundamental wave, and C 0H is the sum of the capacitance of the nonfaulty line. Then, the ratio of the faulty line zero-sequence current to the zero-sequence voltage can be expressed as follows: The ratio of the line zero-sequence current to the zerosequence voltage is related to the impedance of the neutral point branch and capacitance of the nonfaulty line. Next, the relationship between line zero-sequence current and voltage in the external fault and internal fault conditions is analyzed from the perspective of the time domain.

A. RELATIONSHIP OF THE ZERO-SEQUENCE CURRENT-VOLTAGE FOR AN EXTERNAL FAULT
Considering the influence caused by the line impedance, the relationship between line zero-sequence current and zerosequence voltage is analyzed by a π-type equivalent circuit. Fig. 3 shows the equivalent model of the zero-sequence network of this line under external fault conditions.
The zero-sequence current of the nonfaulty line from the perspective of the time domain is expressed as follows: In (3), L H is the zero-sequence inductance of the sound line, R H is the zero-sequence resistance, C H is the zerosequence capacitance, and u0 is the zero-sequence voltage. In the case of a fault steady state, u 0 = U m cos(ωt + α), i 0H = I mH cos(ωt + β), and it can be approximated that β ≈ α + 90 • and I mH ≈ ωC H U m. Because the capacitive reactance of the line is much larger than the inductive reactance, the current distribution of the line is dominated by the zero-sequence capacitive current. Then, u 0 and i 0H can be defined as follows: Therefore, the ratio of the nonfaulty line zero-sequence current to the differential zero-sequence voltage can be approximately calculated as follows:

B. RELATIONSHIP OF THE ZERO-SEQUENCE CURRENT-VOLTAGE FOR AN INTERNAL FAULT
The zero-sequence current that flows through the line in the case of an internal fault is the vector sum of the neutral point branch current and zero-sequence current of all nonfaulty lines.
In (6), i 0g is the zero-sequence current of the neutral point branch. Since the grounded resistance of the neutral point is much larger than the zero-sequence impedance of the zigzag transformer, to facilitate the calculation, the zero-sequence impedance of the zigzag transformer can be ignored when calculating the zero-sequence current of the neutral point branch. Then, the zero-sequence current of the neutral point branch can be calculated as follows: Similarly, the ratio of the faulty line zero-sequence current to the differential zero-sequence voltage can be approximated VOLUME 11, 2023  as follows:

C. CHARACTERISTIC OF THE RATIO FLUCTUATION COEFFICIENT OF THE ZERO-SEQUENCE CURRENT TO THE DIFFERENTIAL VOLTAGE
Equations (5) and (8) indicate that the factor that affects the difference in the fluctuation range is the difference within the cotangent function. For (5), Assuming that the line resistance is 0.275 /km and the capacitance to ground is 0.0054 µF/km, B H = 5.04e-12 of a 20-km line can be calculated. The low resistance to ground R g is generally 10∼16 ; taking R g = 10 , the ratio can be calculated as 1 3ωR g = 1.06e −4 . Thus, B F ≫ B H . According to these calculation results, ignoring the influence of B H on B F , the difference in ratio fluctuation range of the zero-sequence current to the differential zero-sequence voltage between nonfaulty line and faulty line is shown in Fig. 4.
To measure the difference in the ratio fluctuation range of the zero-sequence current to the differential zero-sequence voltage between nonfaulty line and faulty line, the ratio fluctuation coefficient can be calculated using (9): where P is the fluctuation coefficient, T is the time length of the data window, N is the number of sampling points of the data window, which is equal to the product of the time  length of the data window and sampling frequency, andx is the average value of this segment of data. According to the ratio calculation method of the zerosequence current to differential zero-sequence voltage between nonfaulty line and faulty line in (5) and (8) and through the line zero-sequence current and zero-sequence voltage measured in the PSCAD simulation, the theoretical calculation and simulation results of the ratio absolute value corresponding to the nonfaulty line and faulty line are obtained as shown in Figs. 5 and 6.
The theoretical calculated value and simulated value are basically consistent with the waveform in the same power frequency cycle, but the ratio absolute value of the nonfaulty line at the half-cycle time has a singular point because the differential zero-sequence voltage at the peak moment is 0. As a result, the calculation result of the ratio absolute value is close to positive infinity, the ratio fluctuation of the nonfaulty line is excessively high, and the fluctuation difference of the ratio of the zero-sequence current to the differential zero-sequence voltage that corresponds to the nonfaulty line and faulty line cannot be correctly reflected. Therefore, the detection method in this paper sets a threshold to make the absolute value of the ratio very large to eliminate the singularity.

III. SPGF DETECTION METHOD BASED ON THE RATIO FLUCTUATION COEFFICIENT OF THE LINE ZERO-SEQUENCE CURRENT TO THE DIFFERENTIAL ZERO-SEQUENCE VOLTAGE A. ALGORITHM PRINCIPLE
Quantitative analysis is performed using the discretization calculation method below. We denote the zero-sequence current of the jth sampling point as i 0 (j) and the zero-sequence voltage as u 0 (j); then, the ratio fluctuation coefficient of the zero-sequence current and differential zero-sequence voltage are expressed as follows: In (10), R(j) is the ratio of the zero-sequence current i 0 (j) to the differential zero-sequence voltage corresponding to the jth sampling point. To make the order of magnitude close to 1, the ratio is multiplied by 10 6 .R(j) is the average value of the ratio of the data window corresponding to the jth sampling point, and P(j) is the ratio fluctuation coefficient of the data window corresponding to the jth sampling point.
This analysis indicates that the faulty line has a much larger ratio fluctuation coefficient than the nonfaulty line. Therefore, the SPGF detection criterion in this paper is to detect the faulty line by collecting the line zero-sequence current and zero-sequence voltage in different time periods, calculating the fluctuation coefficient and comparing it with the action setting value. Fig. 7 shows the flow chart of the detection algorithm in this paper. When an SPGF occurs, the zero-sequence voltage abruptly changes. The detection algorithm in this paper uses the magnitude of the sudden change as the starting criterion. When the differential zero-sequence voltage is greater than the setting value u 0.set at a certain sampling time, the ratio R(j) of the zero-sequence current to the differential zerosequence voltage corresponding to each line starts to be calculated. Then, we amend the ratio R(j); i.e., if the difference in zero-sequence voltage before and after the integral time T 1 of the ratio calculation is less than u 0.set , let R(j) = [R(j+1)+R(j-1)]/2. Moreover, we set the absolute value threshold of the ratio to prevent the ratio of the nonfaulty line from being too large. Finally, we calculate the average ratio R ave and fluctuation coefficient P and use 10 m as the data window to calculate the maximum ratio fluctuation coefficient P max . If the ratio fluctuation coefficient P max of a line is greater than the protection action setting value P act , the line occurs an SPGF.

C. PARAMETER SETTING
The detection algorithm based on the ratio fluctuation coefficient of the zero-sequence current to the differential zerosequence voltage proposed in this paper should be realized by setting the following parameters:

1) ZERO SEQUENCE VOLTAGE MUTATION SETTING VALUE U 0.set
This detection algorithm uses the zero-sequence voltage mutation as the starting criterion, so when choosing the zerosequence voltage mutation setting value u 0.set , the magnitude of the zero-sequence voltage and sampling frequency in the high-impedance SPGF should be considered. During the fault transient process, the zero-sequence voltage has a certain oscillation, so u 0.set is set to 0.5 V.

2) DATA WINDOW T TO CALCULATE THE AVERAGE RATIO AND MAXIMUM RATIO FLUCTUATION COEFFICIENT
Considering that the main part of the ratio between zerosequence current and differential zero-sequence voltage in the faulty line is composed of the cot function with a period of 0.01 s, i.e., half a cycle, the length of the time window for data processing is designed to be 0.01 s when calculating the average ratio and maximum ratio fluctuation coefficient so that the output ratio average waveform is more stable.

3) ACTION SETTING VALUE P act
To verify the reliability of the detection algorithm in the 10-kV distribution network system and determine the action VOLUME 11, 2023 For the faulty line, ignoring the influence of B H , B F is calculated as 1.06e-4, and assuming that x is π/8, P F = 60.4. For nonfaulty lines, B H is 3.46e-11, and assuming that x is π/16, it can be calculated that P H = 2.63e-11. Therefore, there is a prominent gap between P F and P H . To facilitate the setting of the action value and consider the influence of the short-circuit fault transient characteristics, P act can be uniformly set to 60.

IV. SIMULATION
According to the 10-kV LRGS in Fig. 8, the model is built using PSCAD/EMTDC for simulation. The model has a total of five feeders, the neutral point grounded resistance is 10 , the sampling frequency is 5 kHz, and the simulation time is 1 s. The line positive sequence and zero sequence parameters of the simulation model are shown in TABLE 1 [22]. The parameters of the transformers are shown in TABLE 2. The leakage reactance of the main transformer and distribution transformer is the positive-sequence leakage reactance, and that of the zigzag transformer is the leakage reactance between the windings.

A. PERFORMANCE ANALYSIS
The simulation sets up three cases with total length L , which are as follows: case 1: L = 10 km, Feeder 1 (0.6 km),   To eliminate the influence of harmonics on the measured signals, butterworth low-pass filter with a base frequency of 200hz is performed for the zero-sequence current and voltage in pscad. Fig. 9 shows the differential zero-sequence voltage waveforms in two periods when a metallic spgf and an spgf with 5000 ω fault resistance occur at the end of feeder 3. Fig. 10 shows the variation curve of the ratio fluctuation coefficient at the end of feeder 3 of the metallic spgf and spgf with 5000-ω faulty resistance when the total length of the outgoing lines of the system is 50 km.
These simulation results reveal that when the total length of the outgoing line is 50 km, the ratio fluctuation coefficient of feeder 3 is greater than the set value, and the action is correct; simultaneously, the coefficient is less affected by the faulty resistance. the ratio fluctuation coefficient of feeder 4 is much lower than the set value, and the action does not malfunction. TABLE 3 shows the ratio fluctuation coefficient of feeder 3 (FL) and feeder 4 (NFL) and the simulation results of the action when the A-phase-to-ground fault occurs. TABLE 3 shows that the detection results of the detection method in this paper are correct for feeder 3 (fl) and feeder 4 (nfl). When the spgf occurs at the head end of the feeder, the nonfaulted line has a larger ratio fluctuation coefficient than that when the fault occurs at other positions. however, the total length of the outgoing line and faulty resistance hardly affect the detection results.
In conclusion, regardless of the change in feeder length, fault position or faulty resistance, the detection algorithm  proposed in this paper can effectively distinguish faulty lines from nonfaulty lines.

B. NOISE DISTURBANCE TEST
The following takes a line with a total outlet length of 50 km as an example to discuss the anti-white noise interference ability of the detection method in this paper and adds Gaussian white noise with a signal-to-noise ratio (SNR) of 20 dB to all measured signals. When the end of feeder 3 is set for 0.2 s, an SPGF with 5000 faulty resistance occurs in phase A. Figs. 11 (a), (b), and (c) compare the waveforms before and after adding white noise to the zero-sequence The simulation results show that after adding white noise with a signal-to-noise ratio of 20 dB to the measurement signal, the ratio fluctuation coefficient of feeder 3 (FL) exceeds the action setting value for half a cycle after the fault, and it is much larger than that of feeder 4 (NFL). The ratio fluctuation coefficient of feeder 4 is always lower than the action setting value. Compared with Fig. 9 (b), after adding white noise interference, the ratio fluctuation coefficient of feeder 3 significantly decreases, but it is still much larger than that of feeder 4 and exceeds the action value. Thus, when an SPGF with high impedance occurs in the line, the white noise interference has a notable effect, but it is not sufficient to affect the detection result. To verify the anti-disturbance capability, the faulty resistance is changed, the A-phase-toground fault is set at different positions of feeder 3, and feeder 4 is used as the observation object of the nonfaulty line. Specific simulation results are shown in TABLE 4.
The ratio fluctuation coefficient of feeder 3 (FL) is always greater than the action setting value, the ratio fluctuation coefficient of feeder 4 (NFL) is always lower than the action setting value, and the noise has little influence on the fault detection. Many simulation results show that the proposed detection method in this paper has good anti-noise disturbance ability.

C. INFLUENCE OF THE LINE PARAMETER ASYMMETRY AND AN UNBALANCED LOAD
To study the influence of the line parameter asymmetry and unbalanced load on the detection method in this paper, the loads of feeders 1 and 5 are set as three-phase unbalanced loads, and other loads are balanced loads based on the 10-kV LRGS in Fig. 8. Feeders 2 and 5 are three-phase-to-ground capacitance parameter asymmetric lines. The unbalanced load and asymmetric line capacitance parameters are shown in TABLE 5 and TABLE 6, respectively.
According to the provisions of the national standard GB/T15543-2008 on the limit of voltage unbalance degree [23], when the power grid is in normal operation, the negative-sequence voltage unbalance degree should not exceed 2% and should not exceed 4% in a short time. The negative-sequence voltage imbalance can be expressed by (12): In (12), U 2 is the root mean square value of the negativesequence component of the three-phase voltage, and U 1 is the root mean square value of the positive-sequence component of the three-phase voltage.
By setting up multiple groups of examples with different fault locations and faulty resistance sizes on the PSACD, the negative-sequence voltage and positive-sequence voltage are obtained through simulation and actual measurement. The corresponding bus negative-sequence voltage imbalance is calculated to be 1.56% using (12), which does not exceed 2% of the specified limit. The specific simulation results are shown in TABLE 7.
To more intuitively reflect the impact of unbalanced loads on grounded faults, taking a distribution network with a total outgoing line length of 50 km as an example, at 0.2 s, an A-phase-to-ground fault occurs at the end of feeder 3 through a faulty resistance of 5000 . The comparison results of SPGF detection in an unbalanced distribution network are shown in Fig. 11. The solid line is the simulation waveform result of the balanced distribution network, and the dotted line is the simulation waveform result of the distribution network with unbalanced load and asymmetric line parameters. Fig. 12 (a) and (b) indicate that compared with the balanced distribution network, when an SPGF occurs in the unbalanced TABLE 4. Fluctuation coefficient and detection results of an A-phase-to-ground fault with an added 20-dB signal-to-noise ratio.  distribution network, the ratio fluctuation coefficient of the line with a three-phase symmetrical parameter is basically unchanged. However, Fig. 12 (c) indicates that the ratio fluctuation coefficient of the line with three-phase asymmetric parameters increases, but this does not affect the detection result of the SPGF. The unbalanced load only affects the magnitude of the zero-sequence components but hardly affects the relationship between the zero-sequence components.

D. HIGH-IMPEDANCE ARC GROUNDING FAULT TEST
High-impedance SPGFs are usually accompanied by the generation of a nonlinear arc. To verify the performance of the detection method in this paper when high-impedance arc grounding faults occur, taking a distribution network with a total outgoing line length of 50 km as the object, feeder 3 is set as the faulty line, and feeder 4 is taken as the observation sample. Arc grounding faults are set at the head end, midpoint and end of the fault line. The arc model adopts the cybernetic model, and the arc equation is expressed as follows: In (13), g arc is the arc conductance; G is the arc stable conductance, whose initial value is 1000 S; C is the time constant; l arc is the arc length, which is set at 10 cm; γ is an empirical constant, which is generally 2.85 × 1e-5; i max is the arc current amplitude, which approximates to the peak current when the arc fault point is directly grounded; i arc is the instantaneous arc current; V g is the steady-state arc voltage gradient, which is 17 V/cm. To simultaneously represent the nonlinear and high-impedance characteristics of the fault, the faulty resistance of the fault branch can be considered the series of the nonlinear arc resistance and fixed resistance. Fig. 13 shows the simulation results when a 2500-arc grounding fault occurs at the end of feeder 3. Compared with a linear high-impedance SPGF, in this case, the ratio   fluctuation coefficient of the faulty line decreases when a high-impedance arc grounding fault occurs, but it is still much higher than the action setting value, while the nonfaulty line hardly changes.
More simulation results are shown in TABLE 8. All ratio fluctuation coefficients of feeder 3 (FL) are greater than the action setting value, and those of feeder 4 (NFL) are smaller than the action setting value, regardless of whether the arc grounding faults occur at the head end, midpoint or end of the line. The proposed detection method can still effectively detect the faulty line under the condition of high-impedance arc grounding fault.

E. COMPARISON WITH TRADITIONAL METHODS
Staged zero-sequence current protection is currently the conventional method to handle grounded faults in the neutral point via an LRGS. The zero-sequence stage-III value should be set to avoid the maximum unbalanced current I unb.max that occurs when the phase-to-phase short circuit occurs at the exit of the next line. The maximum unbalanced current I unb.max and zero-sequence stage-III action setting value can be expressed as follows: In (14), E ϕ is the phase electromotive force of the equivalent power supply of the system, Z s is the impedance between the protection installation and the equivalent power supply of the system behind, Z L is the impedance of the entire length of the protected line, and K rel is the reliability factor and is generally 1.1∼1.2.
To verify the superiority of the detection method proposed in this paper compared with the traditional method, taking the SPGF that occurs at the midpoint of feeder 3 as an example, the cases under different faulty resistances are simulated and analyzed. When the total length of the system outgoing line is 50 km, the faulty resistance is taken as 0, 10 , 50 , 1000 , and 5000 . The results are shown in TABLE 9 in detail.
When the faulty resistance does not exceed 10 , the traditional zero-sequence current protection can detect the fault. When the faulty resistance is 50 , the zero-sequence current at the fault point is lower than the set value, and the fault cannot be detected. The proposed detection method can still detect faulty lines. The detection method in this paper has a better detection effect than the traditional zero-sequence current protection method.

F. COMPARISON WITH OTHER METHODS
To verify the universal applicability of the detection method in this paper, we choose a zero-sequence protection of ratio rule in reference [24] for comparison. Similar to this paper, the zero-sequence protection of ratio rule in reference [24]

FIGURE 14.
Simulation results of the ratio rule in reference [24]. selects a 10-kV LRGS as the research object. When an SPGF occurs on a feeder, the ratio of the sum of zero-sequence current of other feeders and neutral points to the zero-sequence current of this feeder can be calculated to determine whether the fault occurs inside or outside the area. The ratio rule is as follows: In (15), K i is the ratio eigenvalue of the ith feeder,İ i(0) is the zero-sequence current of the ith feeder,İ k(0) is the zero-sequence current of other feeders except ith,İ R n (0) is the zero-sequence current of the neutral point, E i is the average eigenvalue, and n is the number of feeders.
The fault judgement rule is expressed as follows: When E i is less than 10/n, it is determined that the fault occurs in the ith feeder. The method proposed in reference [24] is applicable to cases with high-impedance SPGFs and line parameter asymmetry. The following is an analysis of the performance of the method under the condition of noise disturbance. Taking the distribution network with a total outgoing line length of 50 km and five feeders as an example, it is assumed that a 5000-SPGF occurs at 0.2 s at the end of feeder 3. Gaussian white noise with an SNR of 20 dB is added to the zero-sequence current measured signals, and the waveforms of feeder 3 (FL) and feeder 4 (NFL) are obtained using the ratio rule, as shown in Fig. 14. The results of the proposed method and reference [24] method are compared in TABLE 10.
As shown in Fig. 14, both E 3 and E 4 are greater than the action setting value, so the faulty line cannot be detected. As shown in TABLE 10, when the faulty impedance exceeds 1000 , the method in reference [24] cannot detect the faulty line due to the interference of noise. However, the proposed method maintains good anti-noise ability even under highimpedance SPGF conditions.
Although the zero-sequence protection of the ratio rule proposed in reference [24] can be applied to cases with highimpedance SPGFs and line parameter asymmetry, its performance in anti-noise interference is insufficient. Therefore, the proposed ratio fluctuation coefficient method in this paper can better handle noise disturbance cases.

V. CONCLUSION
This paper proposes a fault detection method based on the ratio fluctuation of the line zero-sequence current and differential zero-sequence voltage. According to the magnitude of the ratio fluctuation coefficient to detect whether a fault occurs, the proposed method only relies on the constraint relationship between the zero-sequence current of the line and the zero-sequence voltage. The principle is simple, and the physical concept is clear. A 10-kV LRGS model was built on the PSCAD/EMTDC simulation platform for verification, and the results show that the fault detection method proposed in this paper has good adaptability in distribution networks with unbalanced loads and asymmetrical parameters. The method can effectively identify SPGFs with linear faulty resistance and has good anti-noise interference ability. Finally, most of the research is based on simulation experiments, which need to be verified by actual engineering field data in the future, and further improve the protection method. The influence of distributed generation on fault characteristics and protection methods deserves further study under the scenario that a high proportion of distributed generation is connected to the distribution network.